Based on observations of the 1982-1983 surge of Variegated Glacier, Alaska, a model of the surge mechanism is developed in terms of a transition from the normal tunnel configuration of the basal water conduit system to a linked cavity configuration that tends to restrict the flow of water, resulting in increased basal water pressures that cause rapid basal sliding. The linked cavity system consists of basal cavities formed by ice-bedrock separation (cavitation), ~1 m high and ~10 m in horizontal dimensions, widely scattered over the glacier bed, and hydraulically linked by narrow connections where separation is minimal (separation gap •< 0.1 m). The narrow connections, called orifices, control the water flow through the conduit system; by throttling the flow through the large cavities, the orifices keep the water flux transmitted by the basal water system at normal levels even though the total cavity cross-sectional area (-200 m2) is much larger than that of a tunnel system (-10 m2). A physical model of the linked cavity system is formulated in terms of the dimensions of the "typical" cavity and orifice and the numbers of these across the glacier width. The model concentrates on the detailed configuration of the typical orifice and its response to basal water pressure and basal sliding, which determines the water flux carried by the system under given conditions. Configurations are worked out for two idealized orifice types, step orifices that form in the lee of downglacier-facing bedrock steps, and wave orifices that form on the lee slopes of quasisinusoidal bedrock waves and are similar to transverse "N channels." The orifice configurations are obtained from the results of solutions of the basal-sliding-with-separation problem for an ice mass constituting a near half-space of linear rheology, with nonlinearity introduced by making the viscosity stress-dependent on an intuitive basis. Modification of the orifice shapes by melting of the ice roof due to viscous heat dissipation in the flow of water through the orifices is treated in detail under the assumption of local heat transfer, which guarantees that the heating effects are not underestimated. This treatment brings to light a meltingstability parameter E that provides a measure of the influence of viscous heating on orifice cavitation, similar but distinct for step and wave orifices. Orifice shapes and the amounts of roof meltback are determined by E. When E •> 1, so that the system is "viscous-heating-dominated," the orifices are unstable against rapid growth in response to a modest increase in water pressure or in orifice size over their steady state values. This growth instability is somewhat similar to the j6kulhlaup-type instability of tunnels, which are likewise heating-dominated. When E <• 1, the orifices are stable against perturbations of modest to even large size. Stabilization is promoted by high sliding velocity v, expressed in terms of a v 4/2 and v-• dependence of E for step and wave cavities. The relationships between basal water pressure and...

The hundredfold speedup in glacier motion in a surge of the kind the kind that took place in Variegated Glacier in 1982-1983 is caused by the buildup of high water pressure in the basal passageway system, which is made possible by a fundamental and pervasive change in the geometry and water-transport characteristics of this system. The behavior of the glacier in surge has many remarkable features, which can provide clues to a detailed theory of the surging process. The surge mechanism is akin to a proposed mechanism of overthrust faulting.

Contrary to what has recently been assumed in modeling the proposed deforming bed mechanism for the rapid motion of Antarctic ice streams, the rheology of water saturated till is probably highly nonlinear, according to information from soil mechanics and preliminary experiments on till from the base of Ice Stream B. The equivalent flow law exponent n is probably as high as ---100, and the nonlinearities of the shear stress and effective pressure dependences are closely linked. The high nonlinearity has important consequences for the deforming bed mechanism. A flow system operating by this mechanism can be unstable as a result of feedback from the generation of basal water by shear heating of basal till. The short-term feedback effect is analyzed for a perturbation in a model ice stream in which the basal meltwater is transported through a distributed system of narrow gap-conduits at the ice-till interface. Although the analysis is approximate and some of the system parameters are poorly known, the results suggest that the deforming bed mechanism is unstable for n >---20. The apparent lack of such an instability in the currently active ice streams implies that their motion is controlled not by the deforming bed mechanism but by some other as yet unidentified mechanism.

The sliding motion of glacier ice over bedrock, which contributes about half the flow velocity of temperate glaciers, is analyzed for arbitrary bedrock topography of low roughness. Fourier‐analyzed topography is represented by a roughness spectral function ζ(h, k) defined in terms of the mean square topographic amplitude. From an essentially exact solution of the sliding problem for linear ice‐flow rheology, an approximate solution for the actual nonlinear rheology is built on the assumption that the second strain‐rate invariant depends only on distance from the ice‐bedrock contact. The transition wavelength λ0 between regelation and plastic flow, constant in the linear theory, is replaced in the nonlinear theory by a velocity‐ and roughness‐dependent parameter λα that plays a similar role. Detailed results are given for three special types of ζ(h, k): (1) white roughness (|ζ| constant); (2) truncated white roughness (|ζ| constant for all wavelengths above a certain lower limit); (3) a single wavelength; and (4) cross‐corrugated sinusoidal waves. The results are tested against field observations of sliding. Given sliding velocity υ, basal shear stress τ, and rheological parameters, the theory predicts roughness values ζ for the different types of ζ(h, k). When compared with ζ values inferred from observed bedrock outcrops, predicted values for white roughness are somewhat too small, whereas for white roughness truncated at 3.53 meters, they are of the expected size (ζ ∼ 0.05). Predicted λα values range from 3 to 112 cm; high υ (>20 m yr−1) generally gives λα in the range 10–40 cm, and low υ (<6 m yr−1) 30–70 cm. The predicted thickness of the regelation layer (1–10 mm) agrees with observation, but the predicted λα values appear to be somewhat too small. Extensive separation of the ice sole from bedrock, due to tensile stresses set up in sliding, is predicted in icefalls, whereas for valley glaciers little separation is predicted, unless meltwater under a head of pressure comparable to half the glacier thickness has access to the bed. Extensive separation is not needed to account for typical sliding velocities, provided that the roughness spectrum is truncated. Observed features of glaciated bedrock indicate truncation, which results from glacial abrasion. For the truncated spectrum, the predicted dependence of υ on τ is much more highly nonlinear than for the full white spectrum; this implies a relatively high sensitivity of sliding velocity to changes in glacier thickness or surface slope.

Satellite radar interferometry (SRI) provides a sensitive means of monitoring the flow velocities and grounding-line positions of ice streams, which are indicators of response of the ice sheets to climatic change or internal instability. The detection limit is about 1.5 millimeters for vertical motions and about 4 millimeters for horizontal motions in the radar beam direction. The grounding line, detected by tidal motions where the ice goes afloat, can be mapped at a resolution of approximately 0.5 kilometer. The SRI velocities and grounding line of the Rutford Ice Stream, Antarctica, agree fairly well with earlier ground-based data. The combined use of SRI and other satellite methods is expected to provide data that will enhance the understanding of ice stream mechanics and help make possible the prediction of ice sheet behavior.

Boreholes drilled to the bottom of ice stream B in the West Antarctic Ice Sheet reveal that the base of the ice stream is at the melting point and the basal water pressure is within about 1.6 bars of the ice overburden pressure. These conditions allow the rapid ice streaming motion to occur by basal sliding or by shear deformation of unconsolidated sediments that underlie the ice in a layer at least 2 meters thick. The mechanics of ice streaming plays a role in the response of the ice sheet to climatic change.

ABSTRACT. Pres ure and tracer measurements in boreholes drilled to the bottom of Ice Strea m B, \\'e t Anta rctica, are used to obtain informa tion about the basal water condu it system in which high water pressures are developed. These high pressures presumably make possible the rapid movement of the ice stream. Pressure in the system is indicated by the borehole water level once connection to the cond uit system is made. O n ini tial connection. here a lso called "breakthrough" to the basal water system, the water level drops in a few minutes to a n initial depth in the range 96-117 m below the surface. These water levels a re near but mostly somewhat deeper than the flotation level of about 100m depth (water level at which ba aJ water pressure a nd ice overburden pressure are equal ), which is calculated from depth-density profil es and is measured in one borehole. The conduit system can be modelled as a continuous or somewhat discontinuous gap between ice and bed; the thickness of the gap 8 has to be about 2 mm to account for the water-level drop on breakthrough, a nd about + mm to fit the results of a salt-tracer experiment indicating downstream transport at a sp eed of 7.5 mm s 1• The above gap-conduit model is, however, ruled out by the way a pressure pulse inj ected into the basal water system at breakthrough propagates outward from the injection hole, and a lso by the large hole-to-hole variation in measured basal pressure, which if p resent in a gap-conduit system with 8 = 2 or 4 mm would result in unacceptably large local water fluxes. An alternative model that avoids the e obj ections, called the "gap opening" model, in\"Oh-e openi ng a gap as injection proceed s: sta rting with a thin film, the injection of water under pressure lifts the ice mass a round the borehole, creating a gap 3 or 4 mm wide at the ice/bed interface. Evaluated quantitatively, the gap-opening model accounts for the volume of water that the basal water y tern accepts on breakthrough, which obviates the gap-conduit model. In order to transport basal meltwater from upst ream it is then necessa ry for the complete hydraulic model to contain also a network of relati\·ely large conduits, of which the most promising type is the ··canal" conduit proposed t heoreticall y by \\"alder and Fowler (1994): flat, low conduits incised into the rill, ,.,_,().J m deep and perhaps rv) m wide, with a fl at ice roof The basal water-pressure data suggest that the canal s are spaced rv5Q-300 m apart, much closer than R-tunnel would be. The deepe t observed water le\·el, 117 m, i the most likely to reflect the actual water pres ure in the canals, corresponding to a basal effective pressure of 1.6 bar. I n th is interpretation, the shallower water levels are affected by loss of hydraulic head in the na rrow passageway(s; that connect along the bed from borehole to cana l (s). Once a borehole has frozen up and any passageways connecting with canals ha\·e become closed, a pressure sensor in contact with the unfrozen till that underlies the ice will measu...

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